Analyzing Concavity of a Function
Key Questions
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For a quadratic function
#f(x)=ax^2+bx+c# ,
if#a>0# , then#f# is concave upward everywhere,
if#a<0# , then#f# is concave downward everywhere.
Questions
Graphing with the Second Derivative
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Relationship between First and Second Derivatives of a Function
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Analyzing Concavity of a Function
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Notation for the Second Derivative
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Determining Points of Inflection for a Function
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First Derivative Test vs Second Derivative Test for Local Extrema
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The special case of x⁴
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Critical Points of Inflection
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Application of the Second Derivative (Acceleration)
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Examples of Curve Sketching